Mechanistic Modeling of Longitudinal Shape Changes: Equations of Motion and Inverse Problems
Ontology highlight
ABSTRACT:
SUBMITTER: Hsieh D
PROVIDER: S-EPMC11008764 | biostudies-literature | 2022 Jan
REPOSITORIES: biostudies-literature
Similar Datasets
Project description:In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of research into incorporating other symmetries into deep learning methods, in the form of group equivariant convolutional neural networks. Much of this work has been focused on roto-translational symmetry of R d , but other examples are the scaling symmetry of R d and rotational symmetry of the sphere. In this work, we demonstrate that group equivariant convolutional operations can naturally be incorporated into learned reconstruction methods for inverse problems that are motivated by the variational regularisation approach. Indeed, if the regularisation functional is invariant under a group symmetry, the corresponding proximal operator will satisfy an equivariance property with respect to the same group symmetry. As a result of this observation, we design learned iterative methods in which the proximal operators are modelled as group equivariant convolutional neural networks. We use roto-translationally equivariant operations in the proposed methodology and apply it to the problems of low-dose computerised tomography reconstruction and subsampled magnetic resonance imaging reconstruction. The proposed methodology is demonstrated to improve the reconstruction quality of a learned reconstruction method with a little extra computational cost at training time but without any extra cost at test time.
| S-EPMC8317019 | biostudies-literature
Project description:In this paper we investigate a variety of deep learning strategies for solving inverse problems. We classify existing deep learning solutions for inverse problems into three categories of Direct Mapping, Data Consistency Optimizer, and Deep Regularizer. We choose a sample of each inverse problem type, so as to compare the robustness of the three categories, and report a statistical analysis of their differences. We perform extensive experiments on the classic problem of linear regression and three well-known inverse problems in computer vision, namely image denoising, 3D human face inverse rendering, and object tracking, in presence of noise and outliers, are selected as representative prototypes for each class of inverse problems. The overall results and the statistical analyses show that the solution categories have a robustness behaviour dependent on the type of inverse problem domain, and specifically dependent on whether or not the problem includes measurement outliers. Based on our experimental results, we conclude by proposing the most robust solution category for each inverse problem class.
| S-EPMC9137882 | biostudies-literature
Project description:ObjectiveThis study aimed to investigate longitudinal deep gray matter (DGM) shape changes and their relationship with measures of clinical disability and white matter lesion-load in a large multiple sclerosis (MS) cohort.Materials and methodsA total of 230 MS patients (179 relapsing-remitting, 51 secondary progressive; baseline age 44.5 ± 11.3 years; baseline disease duration 12.99 ± 9.18) underwent annual clinical and MRI examinations over a maximum of 6 years (mean 4.32 ± 2.07 years). The DGM structures were segmented on the T1-weighted images using the "Multiple Automatically Generated Templates" brain algorithm. White matter lesion-load was measured on T2-weighted MRI. Clinical examination included the expanded disability status scale, 9-hole peg test, timed 25-foot walk test, symbol digit modalities test and paced auditory serial addition test. Vertex-wise longitudinal analysis of DGM shapes was performed using linear mixed effect models and evaluated the association between average/temporal changes of DGM shapes with average/temporal changes of clinical measurements, respectively.ResultsA significant shrinkage over time of the bilateral ventrolateral pallidal and the left posterolateral striatal surface was observed, whereas no significant shape changes over time were observed at the bilateral thalamic and right striatal surfaces. Higher average lesion-load was associated with an average inwards displacement of the global thalamic surface with relative sparing on the posterior side (slight left-side predominance), the antero-dorso-lateral striatal surfaces bilaterally (symmetric on both sides) and the antero-lateral pallidal surface (left-side predominance). There was also an association between shrinkage of large lateral DGM surfaces with higher clinical motor and cognitive disease severity. However, there was no correlation between any DGM shape changes over time and measurements of clinical progression or lesion-load changes over time.ConclusionsThis study showed specific shape change of DGM structures occurring over time in relapse-onset MS. Although these shape changes over time were not associated with disease progression, we demonstrated a link between DGM shape and the patients' average disease severity as well as white matter lesion-load.
| S-EPMC9421532 | biostudies-literature
Project description: Not available
| S-EPMC7617273 | biostudies-literature
Project description:This article concerns the problem of distinguishing human-written and bot-generated texts. In contrast to the classical problem formulation, in which the focus falls on one type of bot only, we consider the problem of distinguishing texts written by any person from those generated by any bot; this involves analysing the large-scale, coarse-grained structure of the language semantic space. To construct the training and test datasets, we propose to separate not the texts of bots, but bots themselves, so the test sample contains the texts of those bots (and people) that were not in the training sample. We aim to find efficient and versatile features, rather than a complex classification model architecture that only deals with a particular type of bots. In the study we derive features for human-written and bot generated texts, using clustering (Wishart and K-Means, as well as fuzzy variations) and nonlinear dynamic techniques (entropy-complexity measures). We then deliberately use the simplest of classifiers (support vector machine, decision tree, random forest) and the derived characteristics to identify whether the text is human-written or not. The large-scale simulation shows good classification results (a classification quality of over 96%), although varying for languages of different language families.
| S-EPMC11784749 | biostudies-literature
Project description:Inferring the properties of a scattering objective by analyzing the optical far-field responses within the framework of inverse problems is of great practical significance. However, it still faces major challenges when the parameter range is growing and involves inevitable experimental noises. Here, we propose a solving strategy containing robust neural-networks-based algorithms and informative photonic dispersions to overcome such challenges for a sort of inverse scattering problem-reconstructing grating profiles. Using two typical neural networks, forward-mapping type and inverse-mapping type, we reconstruct grating profiles whose geometric features span hundreds of nanometers with nanometric sensitivity and several seconds of time consumption. A forward-mapping neural network with a parameters-to-point architecture especially stands out in generating analytical photonic dispersions accurately, featured by sharp Fano-shaped spectra. Meanwhile, to implement the strategy experimentally, a Fourier-optics-based angle-resolved imaging spectroscopy with an all-fixed light path is developed to measure the dispersions by a single shot, acquiring adequate information. Our forward-mapping algorithm can enable real-time comparisons between robust predictions and experimental data with actual noises, showing an excellent linear correlation (R2 > 0.982) with the measurements of atomic force microscopy. Our work provides a new strategy for reconstructing grating profiles in inverse scattering problems.
| S-EPMC8316458 | biostudies-literature
Project description:Inverse problems in image processing, phase imaging, and computer vision often share the same structure of mapping input image(s) to output image(s) but are usually solved by different application-specific algorithms. Deep convolutional neural networks have shown great potential for highly variable tasks across many image-based domains, but sometimes can be challenging to train due to their internal non-linearity. We propose a novel, fast-converging neural network architecture capable of solving generic image(s)-to-image(s) inverse problems relevant to a diverse set of domains. We show this approach is useful in recovering wavefronts from direct intensity measurements, imaging objects from diffusely reflected images, and denoising scanning transmission electron microscopy images, just by using different training datasets. These successful applications demonstrate the proposed network to be an ideal candidate solving general inverse problems falling into the category of image(s)-to-image(s) translation.
| S-EPMC7109091 | biostudies-literature
Project description:Motion, position, and form are intricately intertwined in perception. Motion distorts visual space, resulting in illusory position shifts such as flash-drag and flash-grab effects. The flash-grab displaces a test by up to several times its size. This lets us use it to investigate where the motion-induced shift operates in the processing stream from photoreceptor activation to feature activation to object recognition. We present several canonical, highly familiar forms and ask whether the motion-induced shift operates uniformly across the form. If it did, we could conclude that the effect occurred after the elements of the form are bound. However, we find that motion-induced distortion affects not only the position, but also the appearance of briefly presented, canonical shapes (square, circle, and letter T). Features of the flashed target that were closest to its center were shifted in the direction of motion more than those further from its center. Outline shapes were affected more than filled shapes, and the strength of the distortion increased with the contrast of the moving background. This not only supports a nonuniform spatial profile for the motion-induced shift but also indicates that the shift operates before the shape is established, even for highly familiar shapes like squares, circles, and letters.
| S-EPMC10617635 | biostudies-literature
Project description:Brain structural changes in Parkinson's disease (PD) are progressive throughout the disease course. Changes in surface morphology with disease progression remain unclear. This study aimed to assess the volumetric and shape changes of the subcortical nuclei during disease progression and explore their association with clinical symptoms. Thirty-four patients and 32 healthy controls were enrolled. The global volume and shape of the subcortical nuclei were compared between patients and controls at baseline. The volume and shape changes of the subcortical nuclei were also explored between baseline and 2 years of follow-up. Association analysis was performed between the volume of subcortical structures and clinical symptoms. In patients with PD, there were significantly atrophied areas in the left pallidum and left putamen, while in healthy controls, the right putamen was dilated compared to baseline. The local morphology of the left pallidum was correlated with Mini Mental State Examination scores. The left putamen shape variation was negatively correlated with changes in Unified Parkinson's Disease Rating Scale PART III scores. Local morphological atrophy of the putamen and pallidum is an important pathophysiological change in the development of PD, and is associated with motor symptoms and cognitive status in patients with PD.
| S-EPMC10980751 | biostudies-literature
Project description:We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by Partial Differential Equation (PDE) models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach.
| S-EPMC5352987 | biostudies-literature